Rotor with asymmetric blade spacing

ABSTRACT

A turbine apparatus comprises a rotor with a hub section defined about a rotational axis and a plurality of blades attached to the hub section. The plurality of blades comprises a first group having a first angular spacing in a first circumferential sector of the rotor, and a second group having a second angular spacing in a second circumferential sector of the rotor. The first angular spacing is different from the second angular spacing, and the rotor blades are asymmetric about the rotational axis.

BACKGROUND

This invention relates generally to turbine and compressor systems, and specifically to rotor noise reduction. In particular, the invention concerns noise reduction for compressor rotors, impellers and other turbomachinery components, including compressor and impeller rotors for auxiliary power units or APUs.

Turbine engines are utilized in a wide range of applications including electrical power generation, aviation, and industrial heating and cooling. The turbine core is built around a compressor section in flow series with a combustor and turbine section, with an upstream inlet and downstream exhaust. The compressor section compresses air from the inlet, which is mixed which fuel in the combustor and ignited to generate hot combustion gas. The turbine section extracts energy from the expanding combustion gas, which is then discharged through the exhaust. Some of the energy is used to drive the compressor section, and the excess is delivered in the form of rotational motion or propulsive thrust, or a combination thereof.

The compressor and turbine sections each include a number of rotor blade and stator vane airfoils, which are arranged in a series of alternating blade and vane stages. In large-scale engines, two, three or more sections may be coaxially arranged into high, low and intermediate pressure spools, which can rotate at different speeds, and in different directions.

In ground-based industrial gas turbines, the output or power shaft is coupled to an external load such as an electrical generator, or to a pump, blower or other rotary apparatus. In aviation applications, the low-spool is coupled to a propeller (turboprop engines) or a propulsion fan (turbofan engines), or to a helicopter rotor or rotary wing (turboshaft engines). Depending on configuration, the coupling may include a gearbox for independent speed control of the fan or output shaft, with respect to the low spool.

Auxiliary power units incorporate smaller-scale (typically one-spool) gas turbine engines, and are used to generate electrical power and run or various auxiliary and accessory systems. In aviation applications, APUs generate electrical power and supply cabin air while the aircraft is on the ground, and provide compressed air to the bleed system for main engine startup. Depending on configuration, APUs can also be employed as in-flight power sources for air conditioning and other environmental control systems, and provide independent or emergency backup power for hydraulics, pneumatics, avionics and flight control.

In each of these applications, the compressor and turbine rotors operate at high speeds. As portions of the blades reach transonic and supersonic velocities, they generate shock waves at the blade passing frequency (BPF), the “pure tone” frequency at which individual blades pass a given fixed point in space.

As a result, gas turbine engines are complex noise sources, and the compressor rotor is a principal noise source. In APUs and other impeller-type rotor applications, the noise is dominated by a discrete tone associated mainly with the BPF, which exceeds the broadband noise portion of the acoustic spectrum. The noise intensity is also a function of aero-acoustic-mechanical interactions between the rotor blades and the working fluid, with multiple tones occurring at harmonics of the engine shaft frequency or engine order. Acoustic energy also shifts and redistributes away from the BPF as the shock fronts propagate away from the rotor and into the far field, resulting in a multi-tone noise spectrum with a characteristic “buzz-saw” like sound quality.

SUMMARY

A turbine apparatus comprises a rotor with a hub section and a plurality of blades. The hub section is defined about a rotational axis, and is divided into first and second circumferential sectors. The blades are attached to the hub section, extending radially outward.

Blades in the first sector have a first angular spacing, and blades in the second sector have a second angular spacing. The first angular spacing is different from the second angular spacing, so that the blades are asymmetric about the rotational axis of the rotor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of a turbomachine with asymmetric rotor blade spacing.

FIG. 2A is a perspective view of a rotor with asymmetric blade spacing, in an even blade number embodiment.

FIG. 2B is a perspective view of a rotor with asymmetric blade spacing, in an odd blade number embodiment.

FIG. 3 is a frequency spectrum plot for a turbomachine rotor.

FIG. 4A is a velocity field contour plot for a rotor with symmetric blade spacing.

FIG. 4B is a velocity field contour plot for a rotor with asymmetric blade spacing.

DETAILED DESCRIPTION

FIG. 1 is a cross-sectional view of turbomachine 10 with asymmetric rotor blade spacing. In this particular embodiment, turbomachine 10 comprises an auxiliary power unit with inlet plenum 12, curvic coupling or shaft 14, load impeller 16 and power head impeller 18. Load impeller 16 and power head impeller 18 co-rotate about turbine axis A, coupled by curvic coupling 14. Load impeller 16 and power head impeller 18 have asymmetric blade spacing to reduce pressure pulsations and vibrations, increasing service life and lowering the environmental noise profile of turbomachine 10.

Inlet plenum 12 divides into load inlet 20 for load impeller 16 (on the left in FIG. 1) and power head inlet 22 for power head impeller 18 (on the right, facing load impeller 16). Air (or another compressible fluid) is drawn through inlet 20 to load impeller 16, which compresses the fluid for a bleed air system or pneumatic reservoir, or for another compressed fluid supply.

Inlet 22 provides air to power head impeller 18, which compresses the air for the combustor section of turbomachine 10. A turbine rotor extracts rotational energy from the expanding combustion gas, driving power head impeller 18 and load impeller 16 via shaft 14. Depending on embodiment, shaft 14 is also coupled to a gearbox, generator or other accessory device.

Impellers 16 and 18 rotate at high speed, generating shock waves at the blade passing frequency. In order to reduce vibrations and lower the characteristic buzz saw noise output profile, rotors 16 and 18 have asymmetric blade spacing. This reduces acoustic energy at the BPF, shifting energy to other engine orders and frequencies.

In dual-rotor embodiments, load impeller 16 and power head impeller 18 have the same number of blades, and load impeller 16 is clocked or rotated on curvic coupling 14 with respect to power head impeller 18. As a result, the load impeller blades rotate out of phase with the power head blades, further reducing noise and vibration effects as described below.

FIG. 2A is a perspective view of rotor 30 for a turbomachine, with asymmetric blade spacing. In this particular embodiment, rotor 30 comprises a load impeller or power head impeller for an auxiliary power unit. Alternatively, rotor 30 comprises an impeller, compressor rotor or a turbine rotor for an APU, turbofan, turboprop or turboshaft engine, or another bladed turbomachine component such as a rotor for a pump, blower or turbine.

Rotor 30 comprises frustoconical hub section 32 with alternating main (long) blades 34 and splitter (short) blades 36. Alternatively, rotor 30 is referred to as a drum or rotor disk (or disc), and hub section 32 may have a generally conical, cylindrical or barrel shape.

In impeller and compressor embodiments, rotor 30 is typically formed of a strong, lightweight metal such as titanium, or a similar alloy. In turbine embodiments, rotor 30 is formed of high-temperature materials such as nickel, cobalt and iron-based alloys or superalloys. Alternatively, rotor 30 is formed from a range of other materials including aluminum, brass and other metals, or from graphite, polymers and composite materials.

Depending on embodiment, blades 34 and splitters 36 (if present) may be integrally formed with hub section 32, for example by molding or by machining a single casting or forging. Alternatively, blades 34 and splitters 36 are separately formed, and attached to hub section 32 by welding, or using a mechanical attachment at the root.

As shown in FIG. 2A, rotor 30 comprises an even number of main blades 34 and splitters 36, for example sixteen. Main blades 34 are circumferentially spaced around rotor 30, extending radially from hub section 32 and axially along rotational axis A. Splitters 36 are interspersed between main blades 34.

Main blades 34 are divided into first 180° sector 38A comprising seven blades 34 with first inter-blade spacing S1≈25.7°, and second 180° sector 38B comprising nine blades 34 with second inter-blade spacing S2≈20.0°. First blade spacing S1 is thus different from second blade spacing S2, in order to reduce vibrations and lower the buzz-saw noise profile by shifting acoustic energy out of the blade passing frequency.

Blade spacing is an angular measurement, extending circumferentially about axis A between the centers or middles of adjacent main blades 34, across splitters 36. In general, the angular separation remains constant, while the actual separation distance between blades 34 varies in the radial direction (that is, away from hub section 32, perpendicular to the rotational axis). Alternatively, angular spacing S1 and S2 differ primarily in the transonic and supersonic regions of blades 34, where the shock waves form. In these embodiments, angular spacing S1 and S2 are defined at a particular span height, for example 90% span height, or at the blade tip (100% span height).

In these embodiments, rotor 30 and hub 32 are divided into two equal circumferential sectors 38A and 38B, with different numbers of blades N1 and N2. Each sector occupies half the rotor circle (that is, 180° in circumferential angle), corresponding to blade spacing S1=180°/N1 and S2=180°/N2, respectively.

For even numbers of blades N, first sector 38A comprises N1=N/2−1 or fewer blades 34 (and splitters 36), and second sector 38B comprises N2=N/2+1 or more blades 34 (and splitters 36). The angular spacing is defined for each of the adjacent blade pairs in the corresponding groups of blades. Blades at the periphery of each sector will have a larger spacing on one side (e.g., toward sector 38A), and a smaller blade spacing on the other side (e.g., toward sector 38B).

In these even-bladed embodiments, the numbers of blades N1 and N2 in sectors 38A and 38B differ by an even number. In the nominal or first-order embodiment, therefore, N1=N/2−1 and N2=N/2+1, with a blade difference of N2−N1=2. In this embodiment, the blade spacing is:

$\begin{matrix} {{{S\; 1({even})} = \frac{180{^\circ}}{{N/2} - 1}},{and}} & \lbrack 1\rbrack \\ {{S\; 2({even})} = {\frac{180{^\circ}}{{N/2} + 1}.}} & \lbrack 2\rbrack \end{matrix}$

In other (higher-order shift) embodiments, the blade numbers may differ by four, six or more, and the blade spacing varies accordingly. It is also possible to divide even numbers of blades and splitters into two equal sets of N1=N2=N/2 blades each, and define unequal circumferential sectors of different angular sizes. In these embodiments, one set of blades occupies more than 180° of the rotor circumference and the other set of blades occupies less than 180°, and the blade spacing varies accordingly.

Splitters 36 are also divided into groups 38A and 38B. Typically, the spacing between adjacent blades 34 and splitters 36 is half the inter-blade spacing, so the inter-splitter spacing in each sector is substantially equal to inter-blade spacing S1 and S2, respectively. Alternatively, splitters 36 are shifted with respect to blades 34, and the inter-blade and inter-splitter spacing vary.

Asymmetric, non-uniform blade spacing goes against the general teachings and common-sense wisdom in the art, which is that blades and splitters should be symmetrically arranged to reduce imbalance. In general, balance is maintained by machining or milling hub section 32 to compensate for mass redistribution due to different blade spacing S1 and S2. Material may either be added or removed, for example on a balance land or balance rim, or along the impeller bore or the back-face of frustoconical portion hub section 32. Alternatively, balance is maintained by drilling or shaping holes in rotor 30, by adding or adjusting balance weights, or via intentional run-out or offset or altering the curvic pitch diameter.

While the angular spacing between blades varies, however, blades 34 may be characterized by a substantially identical geometric profile. In particular, blades 34 of FIG. 2A all have substantially the same mass and stiffness matrix, yielding substantially the same eigenvalues, natural vibration frequencies and corresponding mode shapes. This contrasts with blade mistuning techniques, in which individual blades have different geometric profiles, different mass and stiffness matrices, and different eigenvalues and natural frequencies.

FIG. 2B is a perspective view of alternate rotor 30 for a turbomachine, with asymmetric blade spacing. Rotor 30 comprises hub section 32, main blades 34 and splitters 36.

For odd numbers of blades N, as shown in FIG. 2B, first sector 38A comprises (N−1)/2 or fewer blades 34 (and splitters 36), and second sector 38B comprises (N+1)/2 or more blades 34 (and splitters 36). In this case, the difference in blade number is odd. For the nominal or first-order case N1=(N−1)/2 and N2=(N1+1)/2 (that is, N2−N1=1), the corresponding blade spacing is:

$\begin{matrix} {{{S\; 1({odd})} = \frac{360{^\circ}}{{N - 1}\;}},{and}} & \lbrack 3\rbrack \\ {{S\; 2({odd})} = {\frac{360{^\circ}}{N + 1}.}} & \lbrack 4\rbrack \end{matrix}$

In one particular embodiment, rotor 30 comprises fifteen main blades 34 and fifteen splitters 36, as shown in FIG. 2B. First sector 38A comprises seven blades 34 with angular spacing S1≈25.7°, and second sector 38B comprises eight blades 34 with angular spacing S2≈25.0°. First blade spacing S1 is thus larger than second blade spacing S2, and the blades are asymmetric about the rotor axis.

Asymmetric blade spacing reduces the level of rotor and blade vibrations due to aero-mechanical coupling, and lowers the sound intensity and environmental impact of the acoustic field generated. In particular, asymmetric blade spacing reduces impeller tone noise at the BPF by reducing the Lighthill turbulence stress tensor, as compared to a rotor with a symmetric distribution of the same blade count.

Asymmetric blade spacing also reduces the amplitude of aerodynamic pressure oscillations experienced by the diffuser vanes, maintaining vane integrity by reducing resonance effects at the natural vibration frequencies. In particular, asymmetric blade spacing reduces the amplitude of pressure excitations though harmonic effects, decreasing the likelihood of high cycle fatigue (HCF) damage or failure, which can occur when cyclic stresses exceed the endurance limits of the vane material. Vibration effects are further reduced by out of phase synchronization of multiple rotors, as further described below.

FIG. 3 is a frequency spectrum plot for a turbine rotor. Frequency is given along the horizontal axis, with magnitude along the vertical, both in arbitrary units. Frequency peaks are labeled by engine order (EO).

Sources of rotor vibration can be traced to two main categories or types: mechanical and aerodynamic. Mechanical causes are related to dynamic characteristics of the rotor, and are influenced by a number of factors including unbalance, bearing support misalignment, shaft run out, and damaged or rubbing parts. Aerodynamic causes are related to pressure pulsations at discrete multiples of the rotor rotational frequency and number of blades (i.e., multiples of the BPF). Aerodynamic sources originate in disturbances generated by blades 34, which are transmitted to rotor 30.

In the rotor frequency spectrum, the first engine order (1EO) represents the effect of rotor imbalance. The second, third, fourth, sixth, eighth and other harmonics are due to mechanical factors, as described above. A rotor or impeller with sixteen main blades, for example, will exhibit dynamic effects characterized by the second (2EO), fourth (4EO) and eighth engine orders (8EO), due to the common factors of two, four and eight. A rotor or impeller with fifteen main blades will exhibit dynamic effects characterized by the third (3EO) and fifth engine orders (5EO), due to the common factors of three and five.

The acoustic field is described by an inhomogeneous wave equation, which can be derived from the Navier-Stokes equations. Using Einstein notation:

$\begin{matrix} {{{\frac{\partial^{2}\rho}{\partial t^{2}} - {c_{0}^{2}{\nabla^{2}\rho}}} = \frac{\partial^{2}T_{ij}}{{\partial x_{i}}{\partial x_{j}}}},} & \lbrack 5\rbrack \end{matrix}$

where ρ is the air or fluid density, c₀ is the ambient sound speed and T_(ij) is the Lighthill turbulence stress tensor. Sound (noise) generation is attributed to the right hand side of this equation.

The Lighthill stress tensor is further defined by:

T _(ij) =ρv _(i) v _(j)−σ_(ij)+(p−c ₀ ² p)δ_(ij),  [6]

with velocity components v_(i) and v_(j), viscous stress contribution σ_(ij) and pressure p. The term ρv_(i)v_(j) is the Reynolds stress tensor, representing unsteady convention of flow. Viscous stress tensor σ_(ij) represents the sound generated by shear, and pressure p is incorporated into the non-linear acoustic or sound generation term (p−c₀ ²ρ), with Kronecker delta δ_(ij) defined to be one for i=j and zero for i≠j.

Bladed turbine components generate pressure pulsations with a strong discrete component at the blade passing frequency, for example at a BPF corresponding to 15EO or 16EO, depending on the blade count. For a rotor having dynamic characteristics expressed in harmonics of the engine order, the BPF amplitude will in general influence rotor stability.

In a rotor with asymmetric blade spacing, the periodic and cyclic pressure field characteristics are reduced by the introduction of two blade sectors having different numbers of blades N1 and N2, with different angular spacing S1 and S2. The pressure function is expressed in terms of a Fourier series of in the BPF frequency:

P(t)=P ₀+α₁ sin(1EO×t+α ₁)+ . . . +α_(N) sin [(N)EO×t+α _(N)]+ . . .  [7]

The coefficients a_(n) represent the relative amplitudes of the sine function at each engine order, and at relative phase α_(n). Index n runs from n=1 for first engine order 1EO, through harmonics of order n=N and above.

In an odd-numbered asymmetric configuration with N1=(N−1)/2 blades at spacing S1 and N2=(N+1)/2 blades at spacing S2, there are substantial contributions to engine orders 2N1=N−1 and 2N2=N+1:

$\begin{matrix} {{P(t)} = {P_{0} + {b_{1}{\sin \left( {{1E\; 0 \times t} + \beta_{1}} \right)}} + \ldots + {b_{N - 1}{\sin \left\lbrack {{\left( {N - 1} \right){EO} \times t} + \beta_{N - 1}} \right\rbrack}} + {b_{N}{\sin \left\lbrack {{(N){EO} \times t} + \beta_{N}} \right\rbrack}} + {b_{N + 1}{\sin \left\lbrack {{\left( {N + 1} \right){EO} \times t} + \beta_{N + 1}} \right\rbrack}} + \ldots}} & \lbrack 8\rbrack \end{matrix}$

In particular, the asymmetric configuration possesses the following aerodynamic pressure amplitude characteristics:

$\begin{matrix} {{{a_{N - 1}({asymmetric})} < {\frac{1}{1 + ɛ}{b_{N - 1}({symmetric})}}},} & \left\lbrack {9A} \right\rbrack \\ {{{a_{N}({asymmetric})} < {\frac{1}{1 + ɛ}{b_{N}({symmetric})}}},{and}} & \left\lbrack {9B} \right\rbrack \\ {{a_{N + 1}({asymmetric})} < {\frac{1}{1 + ɛ}{{b_{N + 1}({symmetric})}.}}} & \left\lbrack {9C} \right\rbrack \end{matrix}$

The difference or amplitude reduction coefficient (c) is about thirty percent (30%) or more (that is, ε≧0.30). Conversely, therefore, unmodified (symmetric) amplitudes b_(N−1), b_(N) and b_(N+1) are at least 30% greater than modified (asymmetric) amplitudes a_(N−1), a_(N) and a_(N+1).

For the case of a fifteen blade (fifteen splitter) rotor divided into two groups or sectors of seven and eight blades, respectively, the first sector of seven blades generates a BPF pressure signal at engine order 14EO (i.e., 2×7), and the second sector of eight blades generates a BPF pressure signal at engine order 16EO (i.e., 2×8). This gives:

$\begin{matrix} {{a_{14} < {\frac{1}{1 + ɛ} \times b_{14}}},} & \left\lbrack {10A} \right\rbrack \\ {{a_{15} < {\frac{1}{1 + ɛ} \times b_{15}}},{and}} & \left\lbrack {10B} \right\rbrack \\ {a_{16} < {\frac{1}{1 + ɛ} \times {b_{16}.}}} & \left\lbrack {10C} \right\rbrack \end{matrix}$

The reduction factor is at least 30% in these engine orders, as described above.

For even blade counts N, the rotor is divided into a first sector with N1=N/2−1 blades at spacing S1, and a second sector with N2=N/2+1 blades at spacing S2. Asymmetric contributions appear at engine orders (N−2)EO and (N+2)EO:

P(t)=P ₀ +b ₁ sin(1EO×t+β ₁)+ . . . +b_(N−2) sin [(N−1)EO×t+β _(N−2) ]+ . . . +b _(N) sin [(N)EO×t+β _(N) ]+ . . . +b _(N+2) sin [(N+1)EO×t+β _(N+2)]+ . . .  [11]

Amplitude reduction is again at least 30%, giving:

$\begin{matrix} {{{a_{N - 2}({asymmetric})} < {\frac{1}{1 + ɛ}{b_{N - 2}({symmetric})}}},} & \left\lbrack {12A} \right\rbrack \\ {{{a_{N}({asymmetric})} < {\frac{1}{1 + ɛ}{b_{N}({symmetric})}}},{and}} & \left\lbrack {12B} \right\rbrack \\ {{a_{N + 2}({asymmetric})} < {\frac{1}{1 + ɛ}{{b_{N + 2}({symmetric})}.}}} & \left\lbrack {12C} \right\rbrack \end{matrix}$

For a sixteen-blade rotor divided into sectors of seven and nine blades, respectively, the first sector generates an excitation BPF at engine order 14EO (2×7 blades), and the second sector generates an excitation BPF at engine order 18EO (2×9 blades). Thus

$\begin{matrix} {{a_{14} < {\frac{1}{1 + ɛ} \times b_{14}}},} & \left\lbrack {13A} \right\rbrack \\ {{a_{16} < {\frac{1}{1 + ɛ} \times b_{16}}},{and}} & \left\lbrack {13B} \right\rbrack \\ {a_{18} < {\frac{1}{1 + ɛ} \times {b_{18}.}}} & \left\lbrack {13C} \right\rbrack \end{matrix}$

In a turbomachine with two or more rotors, each rotor contributes to the total pressure amplitude. For co-rotating load and power head impellers having the same number of blades N, for example, the net pressure signal is:

$\begin{matrix} {{P(t)} = {P_{0} + {c_{1}{\sin \left( {{1{EO} \times t} + \beta_{1}} \right)}} + \ldots + {c_{N}{\sin \left\lbrack {{(N){EO} \times t} + \beta_{N}} \right\rbrack}} + \ldots + {d_{1}{\sin \left( {{1{EO} \times t} + \gamma_{1}} \right)}} + \ldots + {d_{N}{\sin \left\lbrack {{(N){EO} \times t} + \gamma_{N}} \right\rbrack}} + \ldots}} & \lbrack 14\rbrack \end{matrix}$

Primary (first) engine order 1EO is defined by the blade passing frequency, which depends on blade number N and angular frequency w:

1EO≡BPF=Nω.  [15]

For asymmetric blade spacing at odd blade numbers N, “side-band” harmonic contributions appear at engine orders (N±1)EO. For even blade numbers N, contributions appear at engine orders (N±2)EO.

Frequency-compatible rotors have the same number of blades N, divided into similar sets of blades N1 and N2 with similar blade spacing S1 and S2, giving the same BPF excitation frequencies. In order to shift the two contributions out of phase, one rotor is clocked or rotated about by an angle of 360°/2N about the engine axis. This yields:

γ_(n)=β_(n)=π.  [16]

In general, two signals of the same frequency having the same amplitude facing each other (or counter-propagating) can be canceled or negated by placing them out of phase (or in destructive interference). The magnitude or amount of the phase shift is a function of wavelength and the distance between of the two sources. Mechanically, the phase shift is accomplished via the shaft or linkage connecting the two impellers to the rotor assembly. For curvic couplings, for example, the curvic “teeth” structures (castellations or notches) are typically aligned at either end, and the angular offset is accomplished by rotating one of the impeller rotors with respect to the teeth.

In one particular embodiment, the curvic coupling has 2N notches or curvic teeth (that is, twice the blade number). In this embodiment, one of the impellers is rotated by one tooth or notch, producing an angular offset of 360°/2N to generate the required phase shift. Alternatively, the impeller is rotated by an odd number of teeth.

In principle, equally loaded rotors will have substantially similar amplitude coefficients c_(n) and d_(n), and the net pressure field may approach zero at some points. In practice, however, the rotors are not always the same size, and do not experience the same loading, so the amplitudes are different. In addition, the relative phase shift varies by location, generating a standing wave pattern in (at least) the near and intermediate fields.

These effects are addressed by controlling tip clearance, housing eccentricity, rotor run-out and blade stiffness to produce rotors with substantially equivalent impendence. This further minimizes the net pressure signal, including the far field region where environmental effects are a concern.

FIG. 4A is a velocity field plot for rotor 30 with symmetric spacing of blades 34 and splitters 36 about hub 32, and FIG. 4B is plot for asymmetric spacing. Both plots are taken at 95% blade span, with the Mach contours shown in arbitrary units.

Flow separation zones FZ correspond to low Mach numbers of about M≦0.30 or M≦0.15, and are associated with acoustic source strength. Comparing FIG. 4A to FIG. 4B, flow separation for asymmetric blade spacing (FIG. 4B) is weaker than for the symmetric case (FIG. 4A), and flow separation zones FZ are reduced in size. Thus, for the same blade count, asymmetric blade spacing (FIG. 4B) induces relatively lower sound intensity than symmetric blade spacing (FIG. 4A).

While this invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention. In addition, modifications may be made to adapt a particular situation or material to the teachings of the invention, without departing from the essential scope thereof. Therefore, the invention is not limited to the particular embodiments disclosed herein, but includes all embodiments falling within the scope of the appended claims. 

1. A turbine apparatus comprising: a rotor having a hub defined about a rotational axis, the hub having first and second circumferential sectors; and a plurality of blades attached to the hub and extending radially therefrom, the plurality of blades comprising a first group of blades having a first angular spacing in the first sector and a second group of blades having a second angular spacing in the second sector; wherein the first angular spacing is different from the second angular spacing, and the rotor blades are asymmetric about the rotational axis.
 2. The turbine apparatus of claim 1, wherein the plurality of blades comprises an odd number N of blades, the first group of blades comprising (N−1)/2 of the N blades and the second group of blades comprising (N+1)/2 of the N blades.
 3. The turbine apparatus of claim 2, wherein the first angular spacing is approximately 360°/(N−1) and the second angular spacing is approximately 360°/(N+1).
 4. The turbine apparatus of claim 1, wherein the plurality of blades comprises an even number N of blades, the first group of blades comprising N/2−1 of the N blades and the second group of blades comprising N/2+1 of the N blades.
 5. The turbine apparatus of claim 4, wherein the first angular spacing is approximately 180°/(N/2−1) and the second angular spacing is approximately 180°/(N/2+1).
 6. The turbine apparatus of claim 1, further comprising a plurality of splitters attached to the hub section and disposed between the plurality of blades.
 7. The turbine apparatus of claim 6, wherein the plurality of splitters comprises a first group of splitters having the first angular spacing in the first circumferential section and a second set of splitters having the second angular spacing in the second circumferential section.
 8. The turbine apparatus of claim 1, wherein the rotor comprises an impeller and further comprising a compressor rotor rotationally coupled to the impeller, the compressor rotor comprising: a compressor hub defined about the rotational axis, the compressor hub having a first and second circumferential sectors; a second plurality of blades attached to the second hub and extending radially therefrom, the second plurality of blades comprising a first group of blades having the first angular spacing in the first sector of the second hub and a second group of blades having the second angular spacing in the second sector of the second hub.
 9. An auxiliary power unit comprising the turbine apparatus of claim 8, and further comprising a curvic coupling for rotationally coupling the second rotor to the first rotor.
 10. An auxiliary power unit comprising the turbine apparatus of claim 8, wherein the first rotor is clocked with respect to the second rotor such that the first plurality of blades is out of phase with respect to the second plurality of blades.
 11. An impeller comprising: a hub section defined about a rotational axis, the hub section comprising first and second circumferential sectors; a first set of blades extending radially from the first sector of the hub section, the first set of blades having a first angular spacing; and a second set of blades extending radially from the second sector of the hub section, the second set of blades having a second angular spacing; wherein the first angular spacing is different from the second angular spacing, such that the first and second sets of blades are asymmetric about the rotational axis.
 12. The impeller of claim 11, wherein the first set of blades comprises an odd number of blades N1 and the first angular spacing is about 180°/N1.
 13. The impeller of claim 12, wherein the second set of blades comprises an even number of blades N1+1 and the second angular spacing is about 180°/(N1+1).
 14. The impeller of claim 12, wherein the second set of blades comprises an odd number of blades N1+2 and the second angular spacing is about 180°/(N1+2).
 15. An auxiliary power unit comprising the impeller of claim
 11. 16. The auxiliary power unit of claim 15, further comprising a compressor rotor rotationally coupled to the impeller, the compressor rotor comprising: a compressor hub defined about the rotational axis, the compressor hub comprising first and second circumferential sectors; a third set of blades extending radially from the first sector of the compressor hub, the third set of blades having the first angular spacing; a fourth set of blades extending radially from the second sector of the compressor hub, the fourth set of blades having the second angular spacing.
 17. A turbomachine comprising: a load impeller circumferentially divided into first and second sectors, the first sector of the load impeller having a set of blades with a first angular spacing and the second sector of the load impeller having a set of blades with a second angular spacing; a power head impeller circumferentially divided into first and second sectors, the first sector of the power head impeller having a set of blades with the first angular spacing and the second sector of the power head impeller having a set of blades with the second angular spacing; and a rotational coupling between the load impeller and the power head impeller, the coupling defining a rotational axis; wherein the first angular spacing and the second angular spacing are different, such that the load impeller and the power head impeller are asymmetric about the rotational axis.
 18. The turbomachine of claim 17, wherein the load impeller is clocked about the rotational axis with respect to the power head impeller, such that the load impeller is out of rotational phase with respect to the power head impeller.
 19. The turbomachine of claim 17, wherein the load impeller and the power head impeller each comprise an equal, odd number of blades N, and wherein the first angular spacing is about 360°/(N−1) and the second angular spacing is about 360°/(N+1).
 20. The turbomachine of claim 17, wherein the load impeller and the power head impeller each comprise an equal, even number of blades N, and wherein the first angular spacing is about 180°/(N/2−1) and the second angular spacing is about 180°/(N/2+1). 